Let P be a prime ideal in a commutative ring R and let S = R\P, i.e.
the complement of P in R. Pick out the true statements:
(a) S is closed under addition.
(b) S is closed under multiplication.
(c) S is closed under addition and multiplication

-1 for using the imperative "pick out the true statements" in a question addressed to actual people, which contribute here just for fun. We're not obliged to answer you. Consider giving your question a friendlier tone (e.g. "Please help me picking out the true statements..."), and some background on what you've tried.
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Nils MatthesSep 18 '12 at 10:28

1

I don't care. I'm used to mathematical questions stated in the imperative. And I don't think I answer questions only for the questioners. There are several reasons why I answer(e.g. for fun, for reps, just bored, etc.).
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Makoto KatoSep 18 '12 at 10:38

Can you tell us your thoughts on the problem?
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Alex BeckerSep 19 '12 at 19:11